Dahn Jahn
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 Mar 3 comment Is knowledge of PDE useful for SDE? @BCLC: This one and math.stackexchange.com/questions/988098/… are two questions that are relevant, but seem restricted (i.e. asking about particular problem, not the two fields) and not very accessible to someone who knows next-to-nothing about PDE (and not much about SDE either) Mar 3 asked Is knowledge of PDE useful for SDE? Feb 24 awarded Notable Question Feb 10 comment How to put my knowledge of probability and statistics to practice Yes, I do definitely agree, actually learning molecular biology next semester :) Feb 10 comment How to put my knowledge of probability and statistics to practice Thank you for this answer! To be honest, I have a small aversion towards statistics, but I did not include that into the question, as I know overcoming this aversion is necessarily part of learning to work with data. Dalgaard's book sounds perfect, especially since my main goal is to go to biology/medicine after I finish my masters. I have a marginal pop-ed interest in big data, but feel like if I ever go into it, it will only be after having solid basics in other ways of handling data. Feb 10 revised How to put my knowledge of probability and statistics to practice added 23 characters in body Feb 10 asked How to put my knowledge of probability and statistics to practice Feb 1 accepted Conditional probability and almost sure equality confusion Jan 30 awarded Nice Answer Jan 25 comment Conditional probability and almost sure equality confusion Well I follow your reasoning, which means I can now prove my original statement (with the added measurability), yet I feel I am no closer to the understanding. Is there anything more you could say on this? I suppose the intuition is what I largely lack and what makes me feel like I don't actually understand any of it. Jan 25 comment Conditional probability and almost sure equality confusion @sinbadh I agree that if $X$ is $\mathcal G$-measurable, we get that equality. But I'm talking about $Y$ - if $Y$ is $\mathcal G$-measurable, I don't see how we get the equality $Y\stackrel {a.s.} = E^{\mathcal G} X$directly from the definition of conditional expectance. Jan 25 comment Conditional probability and almost sure equality confusion Ah! We might be gettting somehwere. Or at least I am, you already are "somewhere". In an hour I'll sit down with this and see if I can now clear the mess in my mind. Jan 25 revised Conditional probability and almost sure equality confusion added 60 characters in body Jan 25 comment Conditional probability and almost sure equality confusion @BCLC: Well I didn't, by "is such that" I only wanted to include the (what seemed to me as) relevant part of the definition, keeping in mind that we all know that it has to be measurable. I'll add that to the question. Jan 25 comment Conditional probability and almost sure equality confusion Thanks. This might be the problem. When you say $Y=Z$ in the $P$-a.s. sense in relation to $\mathcal G$, does this mean that in the context a.s. means with relation to $\mathcal G$ and not $\mathcal F$? I don't see why. Jan 25 comment Conditional probability and almost sure equality confusion Thanks, that clears some of the confusion (and possibly answers this question). Could you elaborate on why the measurability is sufficient? Jan 25 revised Conditional probability and almost sure equality confusion added 6 characters in body Jan 25 asked Conditional probability and almost sure equality confusion Jan 10 accepted Limit of a random walk with zero mean Jan 10 comment Limit of a random walk with zero mean Ah, dammit. Well, thank you :)